Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 3x - 2$ and $ KL = 5x - 14$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {3x - 2} = {5x - 14}$ Solve for $x$ $ -2x = -12$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 3({6}) - 2$ $ KL = 5({6}) - 14$ $ JK = 18 - 2$ $ KL = 30 - 14$ $ JK = 16$ $ KL = 16$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {16} + {16}$ $ JL = 32$